Question

The length of a rectangular floor is 3 meters less than three times its width. If a diagonal of the rectangle is 13 meters, find the length and width of the floor.
width m

Answer 1

if length of rectangular floor is l, width is m and diagonal is n
then l=3m-3
by Pythagoras theorem,
l^2+m^2=n^2
(3m-3)^2+m^2=13^2
9m^2+9-18m+m^2=169
10m^2-18m-160=0
by solving,
m=5
width-m=5 meters
length=3m-3=12 meters